To begin with, we note that, following the argument of the proof of Lemma 3.1 in [1]}, the loss function minimized by NFM can be written as
\(L^{NFM}_n = \mathbb {E}_{k\sim \mathcal {S}} L^{NFM(k)}_n\) , where
\( L^{NFM(k)}_n = \frac{1}{n} \sum _{i=1}^n \mathbb {E}_{\lambda \sim \tilde{\mathcal {D}}_{\lambda } } \mathbb {E}_{x_r\sim \mathcal {D}_x } \mathbb {E}_{\xi _k \sim \mathcal {Q}} [h(f_k(g_k(x_i) + \epsilon e_i^{NFM(k)})) - y_i f_k(g_k(x_i) + \epsilon e_i^{NFM(k)})],\) 
